How do you allow inertia in bones for animating in pose mode?
What you want is currently not (simply) available as far as i know.
When animating on the right there is options, there you could enable AutoIk.
Together width that i would use helper empties. So you can set Bone constrains so that for example the feed take 100 height influence of the surfboard, and the hip takes 30%... but it might not realy look 'elastic movement' that way. This is currently still mostly the art of animating.

Perhaps if your handy with python script you could automate the movement or the influence of the helper empties a bit.

Tough yet alone using empty constrains on bones to set their position can reduce work time (if the autoIK bones wont bend wrongly (fix width more constrains)..). Animating by such empties usually does give a better result.